Propagation for Schrödinger Operators with Potentials Singular Along a Hypersurface.

In this article, we study the propagation of defect measures for Schrödinger operators on a Riemannian manifold (, ) of dimension with having conormal singularities along a hypersurface in the sense that derivatives along vector fields tangential to preserve the regularity of . We show that the standard propagation theorem holds for bicharacteristics travelling transversally to the surface whenever the potential is absolutely continuous. Furthermore, even when bicharacteristics are tangential to at exactly first order, as long as the potential has an absolutely continuous first derivative, standard propagation continues to hold.